English
Related papers

Related papers: Toroidal vertex algebras and their modules

200 papers

We change the definition of the vertex representations. As a result the vertex representations has one parameter.

q-alg · Mathematics 2008-02-03 Yoshihisa Saito

We introduce notions of open-string vertex algebra, conformal open-string vertex algebra and variants of these notions. These are ``open-string-theoretic,'' ``noncommutative'' generalizations of the notions of vertex algebra and of…

Quantum Algebra · Mathematics 2009-11-10 Yi-Zhi Huang , Liang Kong

Comparing the bounded derived categories of an algebra and of the endomorphism algebra of a given support {\tau}-tilting module, we find a relation between the derived dimensions of an algebra and of the endomorphism algebra of a given…

Representation Theory · Mathematics 2020-12-08 Yingying Zhang

Using general principles in the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an…

Quantum Algebra · Mathematics 2011-02-01 Benjamin Doyon , James Lepowsky , Antun Milas

We introduce the concept of a triangular representation of a Lie algebra, give a counterpart of Ado's theorem, and discuss $2$-irreducible triangular modules over a nonreductive Lie algebra.

Rings and Algebras · Mathematics 2014-06-24 Keqin Liu

Vertex operator algebras are mathematically rigorous objects corresponding to chiral algebras in conformal field theory. Operads are mathematical devices to describe operations, that is, $n$-ary operations for all $n$ greater than or equal…

High Energy Physics - Theory · Physics 2008-02-03 Yi-Zhi Huang , James Lepowsky

We take a categorical approach to describe ternary derivations and ternary automorphisms of triangular algebras. New classes of automorphisms and derivations of triangular algebras are also introduced and studied.

In this paper we study Weyl modules for a toroidal Lie algebra $\CT$ with arbitrary $n$ variables. Using the work of Rao \cite{1995}, we prove that the level one global Weyl modules of $\CT$ are isomorphic to suitable submodules of a Fock…

Representation Theory · Mathematics 2022-03-04 Sudipta Mukherjee , Santosha Kumar Pattanayak , Sachin S. Sharma

We introduce a notion of Pre-structurable Algebras based upon triality relations and study its relation to structurable algebra of Allison, as well as to Lie algebras satisfying triality.

Rings and Algebras · Mathematics 2013-10-10 Noriaki Kamiya , Susumu Okubo

The aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to the more general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with…

Representation Theory · Mathematics 2007-05-23 Idun Reiten , Claus Michael Ringel

Irreducibilities of Verma modules over a class of Block type Lie algebras are completely determined. The approach developed in the present paper can be used to deal with non-weight modules.

Quantum Algebra · Mathematics 2021-09-02 Qiufan Chen , Jianzhi Han

In this paper, we study Whittaker modules for a Lie algebras of Block type. We define Whittaker modules and under some conditions, obtain a one to one correspondence between the set of isomorphic classes of Whittaker modules over this…

Representation Theory · Mathematics 2009-07-09 Bin Wang , Xinyun Zhu

The purpose of this note is to establish an isomorphism from the vector space of extensions between two modules over a vertex algebra, to an appropriate first chiral homology of one dimensional projective space with coefficients in the…

Quantum Algebra · Mathematics 2024-08-14 Thadeu Henrique Cardoso , Jethro van Ekeren , Juan Guzman , Reimundo Heluani

We complete a classification of the two-vertex geometrically irreducible algebras. We also classify the algebras in new classes of hom- and ext-irreducible algebras.

Representation Theory · Mathematics 2024-05-08 Grzegorz Bobinski , Grzegorz Zwara

Mirror Symmetry for Calabi-Yau hypersurfaces in toric varieties is by now well established. However, previous approaches to it did not uncover the underlying reason for mirror varieties to be mirror. We are able to calculate explicitly…

Algebraic Geometry · Mathematics 2009-10-31 Lev A. Borisov

An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut

Rings and Algebras · Mathematics 2018-03-14 Victor Zharinov

Geometric vertex algebras are a simplified version of Huang's geometric vertex operator algebras. We give a self-contained account of the equivalence of geometric vertex algebras with Z-graded vertex algebras.

Quantum Algebra · Mathematics 2026-01-06 Daniel Bruegmann

The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as…

Rings and Algebras · Mathematics 2013-01-10 Ievgen Makedonskyi , Anatoliy Petravchuk

This paper studies certain relations among vertex algebras, vertex Lie algebras and vertex Poisson algebras. In this paper, the notions of vertex Lie algebra (conformal algebra) and vertex Poisson algebra are revisited and certain general…

Quantum Algebra · Mathematics 2007-05-23 Haisheng Li

A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.

Rings and Algebras · Mathematics 2018-08-29 Victor Zharinov